Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Fractional differentiation and Lipschitz spaces on local fields

Author: C. W. Onneweer
Journal: Trans. Amer. Math. Soc. 258 (1980), 155-165
MSC: Primary 43A70; Secondary 26A33
MathSciNet review: 554325
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we continue our study of differentiation on a local field K. We define strong derivatives of fractional order $\alpha > 0$ for functions in ${L_r}(\textbf {K})$, $1 \leqslant r < \infty$. After establishing a number of basic properties for such derivatives we prove that the spaces of Bessel potentials on K are equal to the spaces of strongly ${L_r}(\textbf {K})$-differentiable functions of order $\alpha > 0$ when $1 \leqslant r \leqslant 2$. We then focus our attention on the relationship between these spaces and the generalized Lipschitz spaces over K. Among others, we prove an inclusion theorem similar to a wellknown result of Taibleson for such spaces over ${\textbf {R}^n}$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 43A70, 26A33

Retrieve articles in all journals with MSC: 43A70, 26A33

Additional Information

Keywords: Local fields, fractional derivatives, Bessel potentials, generalized Lipschitz spaces
Article copyright: © Copyright 1980 American Mathematical Society